Abstract <p>A mathematical model has been developed to study the formation of uranium deposits in a sandstone layer confined from the top and bottom by weakly permeable rocks. Three types of ore-forming systems were considered. In one system, ore formation is due to the mixing of fluids with different compositions. In this system, the uranium-bearing fluid containing an oxidizing agent flows along the layer while the reducing fluid enters through a fault in the underlying rock. The ore mineralization zone is fully localized in the sandstone and takes one of four characteristic shapes, depending on the system parameters. In the second ore formation system, the uranium-bearing fluid also flows along the layer but spreads partially into the basement rocks in the zone of high fracturing, where the fluid obtains reducing properties. In this case, the ore mineralization zone is predominantly localized in the basement’s fractured rocks, though it can also partially expand into the sandstone layer. The basement rocks in the ore-forming system of the third type are not disturbed; uranium deposition is caused by an ionic absorption process. The first two systems were modeled numerically, and the third system was modeled analytically.</p>